I just recently read Walter Hickey's article in Business Insider, originally published in March 2013, about the 12 most controversial facts in mathematics. Such a list is always subjective, but surprisingly an easy geometric problem is also listed there, namely Varignon's theorem. Hickey calls this fact 'Midpoint parallelograms' and recalls that by drawing a 4 sided polygon and connecting its midpoints you'll get a perfect parallelogram every time.
You can also check the validity of this truth symbolically, that is, you can compare the opposite sides of the black 4 sided polygons. To do so, navigate to the 2nd slide of the presentation, click on the Relation Tool, choose two opposite sites of a black quadrilateral, and click "More..." in the popup window to ask GeoGebra if this fact holds in general.